Each red cell either indexes the 5 in its row or in its column, i.e. it either equals the row of the 5 in its column, or the column of the 5 in its row. For instance, if r3c6 is a 7, then either r7c6 or r3c7 is a 5. Fives are antiknights: no two 5s can be a knight's move apart. Digits in a gray circle must be odd. A white dot joins a consecutive pair of digits.